Lattice-free descriptions of collective motion with crowding and adhesion

Stuart T. Johnston, Matthew J. Simpson, and Michael J. Plank
Phys. Rev. E 88, 062720 – Published 23 December 2013

Abstract

Cell-to-cell adhesion is an important aspect of malignant spreading that is often observed in images from the experimental cell biology literature. Since cell-to-cell adhesion plays an important role in controlling the movement of individual malignant cells, it is likely that cell-to-cell adhesion also influences the spatial spreading of populations of such cells. Therefore, it is important for us to develop biologically realistic simulation tools that can mimic the key features of such collective spreading processes to improve our understanding of how cell-to-cell adhesion influences the spreading of cell populations. Previous models of collective cell spreading with adhesion have used lattice-based random walk frameworks which may lead to unrealistic results, since the agents in the random walk simulations always move across an artificial underlying lattice structure. This is particularly problematic in high-density regions where it is clear that agents in the random walk align along the underlying lattice, whereas no such regular alignment is ever observed experimentally. To address these limitations, we present a lattice-free model of collective cell migration that explicitly incorporates crowding and adhesion. We derive a partial differential equation description of the discrete process and show that averaged simulation results compare very well with numerical solutions of the partial differential equation.

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  • Received 1 October 2013
  • Revised 18 November 2013

DOI:https://doi.org/10.1103/PhysRevE.88.062720

©2013 American Physical Society

Authors & Affiliations

Stuart T. Johnston1,2, Matthew J. Simpson1,2, and Michael J. Plank3

  • 1School of Mathematical Sciences, Queensland University of Technology, Brisbane 4001, Australia
  • 2Tissue Repair and Regeneration Program, Institute of Health and Biomedical Innovation (IHBI), Queensland University of Technology, Brisbane 4001, Australia
  • 3Department of Mathematics and Statistics, University of Canterbury, Christchurch 8140, New Zealand

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Issue

Vol. 88, Iss. 6 — December 2013

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